Diophantine equation for the three-dimensional quantum Hall effect
- 15 June 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 45 (23) , 13488-13493
- https://doi.org/10.1103/physrevb.45.13488
Abstract
When the Fermi level lies in a gap, the Hall conductivity of three-dimensional electrons in a periodic potential is expressed in a topologically invariant form with a set of three integers. If the magnetic fluxes through the three independent areas of the periodic lattice are rational numbers, one obtains a Diophantine equation relating these numbers and the integers which characterize the Hall conductivity.Keywords
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